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Analysis of fractional-order nonlinear dynamic systems under Caputo differential operator
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-04-21 , DOI: 10.1002/mma.7454
Abdullahi Yusuf, Bahar Acay, Mustafa Inc

The current study presents a detailed analysis of two crucial real-world problems under the Caputo fractional derivative in order to deliver some desired results for the ecosystem. In view of the fact that memory effect plays a vital role in the application, we utilize an advantageous non-local fractional operator to investigate and analyze a mathematical model of the planktonic ecosystem and biological system for the ecosystem on Planet GLIA-2. On the other hand, theoretical and numerical results are given for the model created for phytoplankton, which is of great importance in preventing global warming, and the biological model. Existence and uniqueness are discussed for the solutions of both models with the help of the fixed-point theorem under the Caputo operator. Additionally, the first-order convergent numerical technique which is accurate, conditionally stable, and convergent in obtaining the solution of fractional-order nonlinear systems of ordinary differential equations is utilized to simulate the two governing models. Numerical simulations including different values of arbitrary order ρ indicate the righteousness of the conditions for phytoplankton, Jancor, Murrot, and Vekton populations to develop.

中文翻译:

Caputo微分算子下的分数阶非线性动力系统分析

当前的研究对 Caputo 分数阶导数下的两个关键现实问题进行了详细分析,以便为生态系统提供一些理想的结果。鉴于记忆效应在应用中起着至关重要的作用,我们利用有利的非局部分数算子对GLIA-2星球上的生态系统浮游生态系统和生物系统的数学模型进行了调查和分析。另一方面,对防止全球变暖具有重要意义的浮游植物模型和生物模型给出了理论和数值结果。借助卡普托算子下的不动点定理,讨论了两种模型解的存在唯一性。此外,精确的一阶收敛数值技术,条件稳定,并在获得常微分方程的分数阶非线性系统的解时收敛被用来模拟两个控制模型。包括任意阶数不同值的数值模拟ρ表示浮游植物、Jancor、Murrot 和 Vekton 种群发展条件的合理性。
更新日期:2021-04-21
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